Question: Simplify the following expression: $x = \dfrac{p^2 - 12p + 35}{p - 7} $
Explanation: First factor the polynomial in the numerator. $ p^2 - 12p + 35 = (p - 7)(p - 5) $ So we can rewrite the expression as: $x = \dfrac{(p - 7)(p - 5)}{p - 7} $ We can divide the numerator and denominator by $(p - 7)$ on condition that $p \neq 7$ Therefore $x = p - 5; p \neq 7$